Mathematics
The radius of a circle is 17.0 cm and the length of perpendicular drawn from its center to a chord is 8.0 cm. Calculate the length of the chord.
Circles
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Answer
Let AB be the chord of the circle with center O and OC be the perpendicular from center to the chord.
Given,
Radius (OA) = 17 cm
In right angled triangle OAC,
By pythagoras theorem,
⇒ Hypotenuse2 = Perpendicular2 + Base2
⇒ OA2 = OC2 + AC2
⇒ 172 = 82 + AC2
⇒ AC2 = 172 - 82
⇒ AC2 = 289 - 64
⇒ AC2 = 225
⇒ AC = = 15 cm.
We know that,
Perpendicular from center to chord, bisects the chord.
∴ AB = 2 × AC = 2 × 15 = 30 cm.
Hence, length of chord = 30 cm.
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